Discrete Topology Optimization of Structures Without Uncertainty

The objective of topology optimization of a structure is to design its layout optimally. The topology of a structure is defined by its genus or number of handles. When topology of a structure is optimized, its topology might change whenever the material state of the design cell is switched from solid to void or vice versa. This leads to uncertainty fostering ambiguous topology solutions. In order to avoid this uncertainty, discrete topology optimization technique is utilized. In discrete topology optimization procedure all the design cells are considered to be either solid or void, thereby grey cell or intermediate material cells are eliminated and the uncertainty is avoided. Existence of point connections might cause topology uncertainty. This uncertainty can be eradicated through design domain discretization. In optimization process, hexagonal discretization, hybrid discretization, and modified quadrilateral discretization techniques are primarily used to discretize the design domain. In these discretization approaches, any two neighboring cells share an edge and so there will never be point connections. The hybrid discretization is primarily utilized as it has more number of local topology search directions, in comparison to other discretization approaches. However, the topology optimization solutions pertaining to structures are uncertain, if the design domain is discretized differently. This uncertainty is called as mesh dependence problem. In order to eliminate it, the degree of genus (DOG) based topology optimization strategy is introduced. In this strategy, the genus of an optimized structure is constrained during topology optimization process. There exists no topology uncertainty problem even if the design domain is discretized with different discretization approaches. This introduced strategy is used for discrete topology optimization of structures that have multiple loading points. The accuracy of this strategy is demonstrated with some examples